In my post on cross contour drawing I tried to explain how by making marks that moved over a form, you could create a much more powerful expression of the underlying mass that you perceived an object to have. However contour mapping is also used in another area of visualisation, that of electromagnetic fields and space/time diagrams. This type of drawing goes back to Faraday's idea of 'lines of force'. Faraday was an experimenter rather than a mathematician, therefore for someone like myself it is easier to see how his mind was working. He was trying to visualise what happens when two magnets are pushed together. If you have ever tried to do this, you will feel a very powerful push back when you bring like poles together. If you imagine thin hoops of springy metal connecting the two magnets at their north and south poles and then think of how they might bend as you try and push the two magnets together, you get the beginning of an idea of what I think Maxwell was thinking about, especially if the springy metal became more resistant the further you bent it. More recent analogies have used elastic nets to show how gravity creates curves in space, but Maxwell was initially thinking about magnets and the electromagnetic force.
Visualisation of electromagnetic lines of force
Uccello vase
Representation of a cosmic black hole
Lines of force illustrating electromagnetic action
Once Maxwell had begun to turn these ideas into equations, it was evident that both electricity and magnetism were part of the same force, Einstein then at the beginning of the 20th century realises the same equations could help him think about space/time and eventually these what were separate concepts, also become unified.
As an artist what interested me was how Maxwell began to visualise his ideas. He began with thinking about how water flows in a river. Then his ideas of how lines of water might flow were thought of as being analogous to lines of electric force, the velocity of the water being analogous to the intensity of that force. He then thought of dividing the volume of river water into tubes, these could then be seen as lines of flow. The advantage of putting the water into tubes is that you can then measure an amount of flow during any specific time. I.e. so many gallons per second. The idea was that where the river bed widens the cross section of each tube increases, Such a system of tubes, therefore, represent both the direction of motion and velocity of the water at every point, and could correspond, with a system of unit tubes of electric force. In my mind I began to think of a combination between the way iron filings can be used to reveal magnetic forces and how an artist like Leonardo began to visualise flowing water.
As an artist what interested me was how Maxwell began to visualise his ideas. He began with thinking about how water flows in a river. Then his ideas of how lines of water might flow were thought of as being analogous to lines of electric force, the velocity of the water being analogous to the intensity of that force. He then thought of dividing the volume of river water into tubes, these could then be seen as lines of flow. The advantage of putting the water into tubes is that you can then measure an amount of flow during any specific time. I.e. so many gallons per second. The idea was that where the river bed widens the cross section of each tube increases, Such a system of tubes, therefore, represent both the direction of motion and velocity of the water at every point, and could correspond, with a system of unit tubes of electric force. In my mind I began to think of a combination between the way iron filings can be used to reveal magnetic forces and how an artist like Leonardo began to visualise flowing water.
Iron filings follow the lines of force between the poles of a magnet
Leonardo: water in motion
This type of visual thinking continued to evolve. Minkowski visualised Maxwell's mathematics and came up with a series of diagrams that would allow people to visualise events happening within fields. It was these diagrams that were then seen as applicable to space/time as well, thus the idea of fields were seen to be the things that lay behind both gravity and electromagnetism. Einstein's father was an electrical engineer, so he was uniquely positioned to recognise the importance of the electromagnetic field diagrams his father had worked with, when visualising other types of energy fields.
Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. The distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.
Each point in the diagram represents a certain position in space and time, and is called an event.
The world line (yellow path) of a photon, which is at location x = 0 at time ct = 0.
Spacetime diagram of an accelerating observer in special relativity
In the moving diagram above, the vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The small dots are specific events in spacetime.
If we then return to diagrams of black holes we can see both how they relate closely to Uccello's vase drawing and to Maxwell's idea of the way a river widens and narrows to constrict a flow. Even theories about the beginning of the universe can be illustrated by using similar curved nets.
So when drawing mass, perhaps we are also drawing time, both could also be read as a material capturing of energy, the movements of arm and hand, traced in the left over deposits of graphite or ink or charcoal, an intuition of mass, realised via the capture of photons in a brain consisting of electro chemical exchanges that may or may not be subject to sub-atomic interference.
Victor Newsome
'A'
'B'
Victor Vasarely
Occasionally Victor Vasarely touches upon these issues, I often find his work too pedestrian, too much like an art of filling in perspectival shapes in colour but at its best he transcends the process and creates images that are verbs rather than nouns.
A long time ago I wrote about how we used to use what was then called 'giron and fess point' drawing in order to explore how the perception of a situation could be recorded through drawing. Those old posts have been returned to by Mike Croft in south east Asia, who has seen in them a way to open out an understanding of spatial perception in time. See his recent guest drawing blog posts. Now when I come to think about fess points I can see them as nodes, around which different movements oscillate due to certain attractors and this pattern I see as similar to spin networks within quantum space. This could be what has been called 'granularity'. The 'girons' perhaps being more like the lines linking moving nodes in image 'A', the lines of which at one point would have been seen as a way to visualise curved space. Scientists have long sought to bring together particle/wave theories and it would seem that the idea of nodes and events is helping to do this. In the meantime we have also to respond to the need to engage more with the destruction of the natural world and once again I would hope that the more we understand that we are totally entangled with everything else the more we might be inclined to be sensitive to our own actions and thoughts in relation to events, and be less inclined to measure our worth in terms of objects and possessions.
Several of my recent posts have pointed towards a rethinking of the way we view objects and things. Instead of viewing the world as consisting of lots of individual things, I am beginning to see that reality could be simply a series of events. What I have been used to thinking about as discrete things actually being moments of encounter between one thing and another. I shall no doubt be returning to these issues again.
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